can someone help me with this question. and explain it to me.

Question

anonymous · Answer

attachment

ganeshie8 · Answer

remember the `nth term formula` for arithmetic sequence ?

ganeshie8 · Answer

$\large n^{\text{th}} $ term formula :$$\large  a_n =  a_1 + (n-1)d$$

ganeshie8 · Answer

you're given two terms,
plug them in above equation, you will get two equations, solve them

anonymous · Answer

ya

ganeshie8 · Answer

$\large a_{10}=73$

$\large  73 = a_1 + (10-1)d \tag{1}$

ganeshie8 · Answer

$\large a_{28}=235$

$\large  235 = a_1 + (28-1)d \tag{2}$

ganeshie8 · Answer

two equations and two unknonws, you can solve them

anonymous · Answer

would you look for d?

ganeshie8 · Answer

simplify both the equations, what do you get ?

ganeshie8 · Answer

$\large  a_1 + 9d = 73$

$\large  a_1 + 27d = 235$

ganeshie8 · Answer

subtract them vertically and solve $\large d$ first

ganeshie8 · Answer

$\large  a_1 + 9d = 73$

$\large  a_1 + 27d = 235$
--------------------------------
$\large  0 ~-~18d~ = -162$

ganeshie8 · Answer

$\large   -18d~ = -162$

$\large  ~~~~ d = ?$

anonymous · Answer

you can combined them like that?

ganeshie8 · Answer

yes, never heard of elimination method before ?

anonymous · Answer

not for equations like this

ganeshie8 · Answer

well they are just equations like other equations now.
we have translated the original problem into solving system of equations, so you can use ANY of the methods you're familiar with to solve these equations

anonymous · Answer

ok d=9

ganeshie8 · Answer

thats right! plug that value in any of the equations and find out $\large a_1$

anonymous · Answer

-8

ganeshie8 · Answer

$\huge \color{red}{\checkmark}$

anonymous · Answer

your the best